In: Finance
Your sister is the one lucky winner of the Ohio Lottery and is looking to you, as a Finance Major, to help out with some advice. Assuming market interest rates are at 4.00%, on a present value basis how would you consult with her about the choice to
- take an annuity of $2,200 per month for 25 years, or
- take an annuity of $2,400 per month for 20 years ?
- how much is she better off by choosing the one you recommend, remembering that more is better!
The present value of 1st annuity will be as follows:
Present value = Monthly payment x [ (1 – 1 / (1 + r)n) / r ]
r is computed as follows:
= 4% / 12 (Since the payments are on monthly basis, hence divided by 12)
= 0.333333%
n is computed as follows:
= 25 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)
= 300
So, the amount is computed as follows:
= $ 2,200 x [ (1 - 1 / (1 + 0.0033333)300 ) / 0.0033333 ]
= $ 2,200 x 189.4524909
= $ 416,795
The present value of 2nd annuity will be as follows:
Present value = Monthly payment x [ (1 – 1 / (1 + r)n) / r ]
r is computed as follows:
= 4% / 12 (Since the payments are on monthly basis, hence divided by 12)
= 0.333333%
n is computed as follows:
= 20 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)
= 240
So, the amount is computed as follows:
= $ 2,400 x [ (1 - 1 / (1 + 0.0033333)240 ) / 0.0033333 ]
= $ 2,400 x 165.021864
= $ 396,052
So, the first annuity shall be preferred and the same is greater than the 2nd annuity by the amount of:
= $ 416,795 - $ 396,052
= $ 20,743
Feel free to ask in case of any query relating to this question